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We analyze the spatial correlations in the spin density of an electron gas inthe vicinity of a Kondo impurity. Our analysis extends to the spin-anisotropicregime, which was not investigated in the literature. We use an original andnumerically exact method, based on a systematic coherent-state expansion of theground state of the underlying spin-boson Hamiltonian, which we apply to thecomputation of observables that are specific to the fermionic Kondo model. Wealso present an important technical improvement to the method, that obviatesthe need to discretize modes of the Fermi sea, and allows one to tackle theproblem in the thermodynamic limit. One can thus obtain excellent spatialresolution over arbitrary length scales, for a relatively low computationalcost, a feature that gives the method an advantage over popular techniques suchas NRG and DMRG. We find that the anisotropic Kondo model shows rich universalscaling behavior in the spatial structure of the entanglement cloud. First,SU(2) spin-symmetry is dynamically restored in a finite domain in parameterspace in vicinity of the isotropic line, as expected from poor man's scaling.We are also able to obtain in closed analytical form a set of different, yetuniversal, scaling curves for strong exchange asymmetry, which are parametrizedby the longitudinal exchange coupling. Deep inside the cloud, i.e. fordistances smaller than the Kondo length, the correlation between the electronspin density and the impurity spin oscillates between ferromagnetic andantiferromagnetic values at the scale of the Fermi wavelength, an effect thatis drastically enhanced at strongly anisotropic couplings. Our results alsoprovide further numerical checks and alternative analytical approximations forthe recently computed Kondo overlaps [PRL 114, 080601 (2015)].

physical review. b, condensed matter and materials physics

Universal spatial correlations in the anisotropic Kondo screening cloud:  analytical insights and numerically exact results from a coherent state  expansion